Non-selfadjoint matrix Sturm–Liouville operators with spectral singularities

Abstract

In this paper we investigate discrete spectrum of the non-selfadjoint matrix Sturm–Liouville operator L generated in L 2 ( R + , S ) by the differential expression ℓ ( y ) = - y ″ + Q ( x ) y , x ∈ R + : [ 0 , ∞ ) , and the boundary condition y ( 0 ) = 0 . Under the condition sup x ∈ R + exp ε x ‖ Q ( x ) ‖ < ∞ , ε > 0 using the uniqueness theorem of analytic functions we prove that L has a finite number of eigenvalues and spectral singularities with finite multiplicities.